# What is the vertex form of the equation of the parabola with a focus at (-3,-9) and a directrix of #y=-10#?

##### 1 Answer

Feb 11, 2016

#### Explanation:

The vertex of a parabola is always in between the focus and the directrix

From the given, the directrix is lower than the focus. Therefore the parabola opens upward.

p is 1/2 of the distance from the directrix to the focus

vertex #(h, k)=(-3, (-9+(-10))/2)=(-3, -19/2)

see the graph with directrix

graph{((x--3)^2-2(y--19/2))(y+10)=0[-25,25,-13,13]}

have a nice day from the Philippines